It is known that the serum cholesterol level of females is normally distributed and its population variance is 45 mg/100 mL. Researchers decided to estimate the population mean serum cholesterol level. They observed a sample average serum cholesterol level of 220 mg/ml in 35 females.

a. Compute a 95% confidence interval for the population mean serum cholesterol level of females.

b. Researchers at another university are going to collect new data and they are assuming that the female serum cholesterol level is Normally distributed with population variance of 45. How many subjects do they have to observe in order to have a 95% confidence interval with a final length of at most 3?